Tuning Interfacial Concentration Enhancement through Dispersion Interactions to Facilitate Heterogeneous Nucleation

Classical molecular dynamics simulations were used to investigate how dispersion (van der Waals) interactions between non-polar, hydrophobic surfaces and aqueous glycine solutions affect the solution composition, molecular orientation, and dynamics at the interface. Simulations revealed that dispersion interactions lead to a major increase in the concentration of glycine at the interface in comparison with the bulk solution, resulting from a competition between solute and solvent molecules to be or not to be near the interface. This can then lead to kinetic and/or structural effects facilitating heterogeneous nucleation of glycine at non-polar surfaces, in agreement with recent observations for tridecane, graphene, and polytetrafluoroethylene. A novel parameterization process was developed to map a model surface with tunable dispersion interactions to heptane, tridecane, and graphite materials. The model surface was capable of reproducing the solution structure observed in fully atomistic simulations with excellent agreement and also provided good agreement for dynamic properties, at a significantly reduced computational cost. This approach can be used as an effective tool for screening materials for heterogeneous nucleation enhancement or suppression, based on non-specific dispersion interactions based on bulk material molecular properties, rather than interfacial functional groups, templating or confinement effects.

: Diagram of a glycine molecule with each atom labeled with the GAFF atom type used within the simulations. Water molecules were represented using the SPC/E model [3]. The bond lengths and angles were fixed using the SHAKE algorithm. Force field parameters are provided in Table S2. Tridecane molecules were represented using the AMBER-ii [4] force field, which is an extension of the AMBER force field to provide a better description of long chain alkanes. This force field uses the same functional form as GAFF and the force field parameters are provided in Table S3. A charge of -0.012 is assigned to the CH 3 carbons and +0.012 is assigned to the connected CH 2 carbon. All other tridecane atoms are chargeless.
Graphite and PTFE were modelled using GAFF. As the graphite and PTFE atoms were fixed in place and no dynamics were performed, only the intermolecular interactions were required. LJ parameters are provided in Table S4. The carbon atoms of graphite were chargeless, whilst the charges for the PTFE were obtained using the AM1-BCC method within Antechamber [5] and are given in Table S5.   Table S5: Charges assigned to the atoms within the PTFE molecules using the AM1-BCC method.
Backbone Position q C q F  Table S6 shows the system information and simulation times for the glycine solution films used in the MD simulations. The simulation of the bulk solution was performed using the 5.9 nm thick, 296.7 g/kg film, simulated with fully periodic boundaries for 10 ns in the NPT ensemble.

S7
S2 Snapshot of the Tridecane Crystalline Interface

S3 Interface-Atom Parameterisation Example: Tridecane and Nitrogen
In order to provide extra clarity on the LJ parameterisation process, this section will describe how the parameters iw and σ iw were obtained for the interaction between the LJ 9-3 wall representing tridecane and the nitrogen atom within the glycine molecules.
The nitrogen atom within the glycine molecule, n4, has LJ parameters of ii = 0.17 kcal/mol and σ ii = 0.325 nm. 36 evenly spaced positions were selected in the x-y plane of the atomistic, crystalline tridecane slab. A nitrogen atom was placed at a distance, z, of 0.01 nm above the interface at the first x-y position, and the total LJ 12-6 interaction between the tridecane slab and the nitrogen atom was calculated. The distance was then increased in 0.01 nm steps, up to a maximum of z = 1.4 nm, calculating the LJ 12-6 interaction at each step. Figure S3 (a) shows a snapshot of the nitrogen interacting with the tridecane slab.
This provides a z-dependent potential between the atom and the interface, such as the one shown in Figure S3  to better capture the behaviour of the potential well. This does result in deviation from the z-dependent potential at z values close to the interface, however this will not influence the simulation results as atoms will be unable to reach this highly repulsive region under typical conditions. Fitting equation 1 to the data shown in Figure S3 (b) resulted in parameters iw = 1.19 kcal/mol and σ iw = 0.301 nm.
This process was repeated for each of the 36 x-y positions across the face of the tridecane slab, and each of the z-dependent potentials are shown in Figure S3 (c) as the coloured data sets. The average iw and σ iw values are 1.22 kcal/mol and 0.316 nm respectively, and the resulting LJ 9-3 potential is shown as the black line in Figure S3   Diffusion coefficients have been determined for the parallel movement of the glycine molecules within S12 each of the interfacial layers and are plotted for each wall strength in Figure S6. The parallel mobility decreases as ww increases, although for values of ww above 10 kcal/mol the decrease become smaller. This is at least partly due to the concentration of the two layers not increasing significantly for the higher wall strengths as the remainder of the solution is depleted of glycine due to finite size effects. There is a slight decrease in the diffusion coefficient as σ ww increases from 0.17 to 0.51 nm, however this effect is much weaker than is observed for ww , and the diffusion coefficients within the first layer are very similar for σ ww = 0.34 and 0.51 nm. Figure S6: Diffusion coefficients in the x-y direction (parallel to the interface) obtained for the glycine molecules in the first (left) and second (right) interfacial layers for different wall interaction parameters. Figure S9 shows the decay times, as described in section , for the interfacial layers at each wall strength investigated. We see similar behaviour as observed for the diffusion coefficients, with the decay time increasing with ww indicating a reduction in the rotational mobility of the glycine molecules. Once again, a small reduction in the mobility of the molecules is observed for increasing σ ww however, this effect is much less pronounced than observed for ww .   S6 P 2 Profile for 500.7 g/kg, 12 nm Film The simulation of the largest, most concentrated glycine solution film in contact with the LJ 9-3 wall representing graphite resulted in multiple dense layers of glycine at the interface followed by a tailing off region towards the bulk of the film. The P 2 profile, shown in Figure S10, demonstrates that there is not significant ordering of the glycine molecules within the tailing off region. Figure S10: The bond order profile obtained for the 500.7 g/kg, 12 nm glycine solution film in contact with the LJ 9-3 wall representing graphite. The density profile of the glycine solution is plotted on the secondary axis.

S7 Interfacial Region Definition
For simulations of larger and more concentrated glycine solutions, the effects of the interface extends beyond the initially defined 1 nm interfacial region. To account for this, a new method for determining a suitable interfacial region was developed in an attempt to provide a fair comparison between solution films of different sizes and concentrations. A Savitzky Golay filter [6] was used to smooth the density profile as is shown in Figure S11 (a). The filter fits a polynomial to a moving window throughout the data, and was applied using third order polynomials and a window size of five. The filter accurately captures the density profile, but it does slightly understate the peak closes to the interface. However, for determining the interfacial region it is important that the tail down to the bulk-like region is accurately captured, which the Savitzky-Golay filter achieves successfully. The derivative of this smoothed data was taken (see Figure S11 (b)), and the limit of S17 the interfacial region was defined at the point at which this derivative first crosses the x-axis, excluding the interfacial peaks, as is shown by the vertical line. Figure S11: (a) Example of the Savitzky-Golay filter used to smooth the glycine density profile of the 500.7 g/kg, 6.1 nm film prior to taking the derivative. (b) The derivative of the smoothed density profile. The dashed black line represents the point where the derivative crosses the x-axis after the initial peaked area, defining the interfacial region.